Questions tagged [statistical-mechanics]

The study of large, complicated systems by means of statistics and probability theory, in order to extract average properties and to provide a connection between mechanics and thermodynamics.

Filter by
Sorted by
Tagged with
0
votes
1answer
33 views

Nabla Operator in Kinetic Energy Hamiltonian in 2nd Quantization

Why can I, in the 2nd quantisation representation of a kinetic energy Hamiltonian $$ H=\frac { -\hbar ^ { 2 } } { 2 m } \nabla^2 $$ write the Laplace (=Nabla$^2$) operator out like this? $$ \hat { T }...
1
vote
1answer
28 views

Why are the autocorrelations larger for the energy at the critical temperature?

Considering a simulation with the Swendsen-Wang algorithm for the 3-D cubic lattice I wanted to have a look at the auto-correlations, and expecting it to be quite small considering Swendsen-Wang is a ...
1
vote
1answer
3k views

Does the Fermi level depend on temperature?

I know that this question has been asked before (here and here), but there is still something that I cannot understand: The answers in the linked posts clearly state that the Fermi level (level, not ...
0
votes
0answers
38 views

What motivated Gibbs's definition of Gibbs entropy?

What motivated Gibbs's definition of Gibbs entropy? I have read and I think that I agree with the idea that if we have to choose probability distribution for an unknown system then it is a good idea ...
2
votes
1answer
156 views

How can “information” be a useful physical quantity given that its value is model-dependent?

From @Humble's answer to "What is information?": Information contained in a physical system = the number of yes/no questions you need to get answered to fully specify the system. That is, however, ...
0
votes
0answers
49 views

Simple Green's function question: Propagator for stationary particle?

Suppose the probability a particle transitions into a state of interest at time $t$ having position $x$ is $$\omega(x,t).$$ Once a particle enters this state it does not leave it, nor does its ...
2
votes
2answers
63 views

How to explain pressure on a molecular level?

So when I'm on an airplane and I have a bag of chips, at some point when the pressure in the cabin lowers, the bag of chips will bulge up. Here’s how I’d explain this on a molecular level: There are ...
-2
votes
0answers
38 views

Equation of Maxwellian distribution

I have been wondering for a while what function would one use to describe the Maxwellian distribution curve. All that I "think" I am understand is that it has an exponential part. However, that is ...
7
votes
2answers
3k views

Clear up confusion about the meaning of entropy

So I though, and was told, that entropy is the amount of disorder in a system. Specifically the example of heat flow and it flows to maximize entropy. To me this seemed odd. This seemed more ordered ...
0
votes
2answers
442 views

Ideal gas and inelastic collisions

Why is it necessary that all inter-molecular collisions in an ideal gas be elastic? My understanding is that a gas behaves ideally so long as the potential energy arising from inter-molecular ...
2
votes
0answers
41 views

Distance $E_F-E_i$ in a compensated semiconductor

Given two energy level diagrams for a compensated conductor: At $0~\text{K}$ At $500~\text{K}$ I want to determine for which diagram is the Fermi level closest/farthest from $E_i$. It's a ...
0
votes
1answer
26 views

three particles on a state with negative energy have negative temperature?

Suppose three particles on a state with energy $-\epsilon$, that is, $H\lvert\Phi_1\rangle=-\epsilon\lvert\Phi_1\rangle$, as the average energy per particle is $kT$, but is also $-\epsilon/3$, wouldn'...
1
vote
1answer
174 views

What is the difference between these two expressions for the partition function, Z?

What is the difference between these two expressions given for the partition function, Z? $$Z = \sum_{i}e^{-\varepsilon_i/kT}$$ $$Z = \sum_{j} g_je^{-\varepsilon_j/kT}$$ where each energy level has ...
2
votes
1answer
203 views

Ising model as quantum model?

I've read in a few papers things that use the fact that the $2D$ Ising model can be interpreted as a $1+1$ quantum spin model. I haven't been able to find this description and would like to read about ...
1
vote
2answers
42 views

is entropy the same up to a constant?

I have understood that what's important about entropy is its change $\Delta S$, not $S$ itself, much like the electrostatic potential. Therefore, can I assume that a constant entropy can be redefined ...
2
votes
1answer
2k views

Phonon density of states from velocity autocorrelation function

I'm using molecular dynamics and I autocorrelate the velocities and Fourier transform them to obtain the phonon density of states (DOS). I have many doubts about this: The definition of DOS is: ...
0
votes
1answer
59 views

What is the speed of air molecule?

Given the minimal temperature measured in the Earth's atmosphere is not $0\space K$, air molecules are moving. I see no reason for air molecule to move all at the same speed. The question is ...
1
vote
0answers
27 views

Discrepancy when using Saha equation?

I was trying to calculate the level of ionization using Saha eq. for hydrogen gas at 1 atm pressure at 10 000 K and upwards. I used an Excel spreadsheet and the values I get don't match with other ...
0
votes
1answer
28 views

Metropolis Algorithm Transition-Proposal Probability

I'm working my way through a short section on the Metropolis algorithm in the lecture notes on Computational Quantum Physics by Prof. Troyer. However, I am not sure what probability distribution was ...
1
vote
2answers
127 views

Internal energy

Internal energy at a specific state can't be calculated, but using kinetic theory of gases and the law of equipartition of energy, average kinetic energy is directly proportional to temperature. For ...
1
vote
1answer
169 views

Thermodynamic Beta and Inverse Temperature

Following on from my previous question: Exponential form of Boltzmann Distribution I am now trying to understand the relationship between the thermodynamic beta and the inverse temperature. ...
1
vote
1answer
124 views

Bose Einstein Condensation in Grand canonical ensemble

Why we develop formalism of Bose Einstein Condensation in framework of grand canonical ensemble ?
0
votes
2answers
70 views

Does the entropy of a system of two gravitating bodies increase as they get closer together?

It seems like the situation where the two gravitating bodies have collided and coalesced (assuming that they don’t shatter on impact) can be thought of as the ‘equilibrium’ of the system, since this ...
1
vote
2answers
178 views

How to write equation of state in terms of partition function?

While studying quantum gases (fermions, bosons), equation of state written were $PV = k_B T Z_{gr}$, where $Z_{gr}$ is the partition function of grand canonical ensemble. $P$ and $V$ are pressure and ...
18
votes
5answers
2k views

What is temperature on a quantum level?

When I was in high school, I learned that temperature is kinetic energy. When I learned statistical physics, we learned that temperature is a statistical thing, and there was a formula for it. ...
0
votes
0answers
237 views

What are enthalpic and entropic forces?

Am I right when thinking of entropic force to be an entropy minimizing mechanism and enthalpic force to be an energy minimizing mechanism (which is basically an entropy maximization mechanism). What'...
6
votes
4answers
9k views

Mathematical proof of the Second Law of Thermodynamics [duplicate]

Can you formalize statistical mechanics, like some people have done with relativity, and prove the second law of thermodynamics from more foundational axioms?
1
vote
0answers
19 views

Why do the Binder Cumulants of different system sizes intersect at the critical point?

When Monte Carlo simulations are performed for spin models (Ising model etc.) the critical temperature can be found by simulating for different lattice sizes and plotting the Binder Cumulant for them. ...
0
votes
3answers
684 views

Is entropy change same for both closed reversible and irreversible processes?

It is said that entropy is a state function and doesn't depend on path. Also, S(2) - S(1) = ∫đQ/T for reversible process. S(2) - S(1) > ∫đQ/T for irreversible process. 1-> If same amount of heat ...
1
vote
2answers
155 views

Interpretation of Ising model simulations

I've been working on numerically solving the Ising model in a study of phase transitions, but I'm having difficulty finding material to help me discuss the results. I'm studying spontaneous ...
0
votes
4answers
92 views

Thermodynamic definition of entropy describing reversible processes

I've recently started learning about entropy. One possible definition is that it is the logarithm of number of microstates of particles. Another possible definition is that for a reversible (...
1
vote
1answer
25 views

Heisenberg Hamiltonian 2-Spin Terms in Matrix Representation

I am stuck on the interpretation/derivation of the 2-spin terms of the quantum Heisenberg model Hamiltonian. In this model, our electrons, with spin up or down, are confined to sites on a lattice. ...
5
votes
2answers
97 views

Interpretation of density matrix

In Landau’s Statistical Physics (part 1) , section 5, he writes:" In particular, it would be quite incorrect to suppose that the description by means of the density matrix signifies that the subsystem ...
0
votes
1answer
24 views

The strict definition of partition function in continuous system

I am confused about the definition of the partition function. From the class of statistical thermodynamics, I've learned that the partition function for a system with continuous energy can be ...
0
votes
0answers
23 views

Pressure-velocity dispersion relation $p=\rho(r)\sigma^2$

The relation is $p=\rho(r)\sigma^2$. Where $\rho(r) $ is density distribution and $\sigma$ is velocity dispersion(RMSE/root mean square error value). This relation is given for a isotropic velocity ...
1
vote
1answer
213 views

Using Helmholtz Free Energy to Calculate Liquid Density

My objective is to find an equation of state (EoS) for density, i.e. density as a function of pressure, temperature and concentration, for aqueous acids, bases and salts. A StackExchange user ...
2
votes
0answers
59 views

What is the meaning of complex-valued entropy?

I was wondering, from Boltzmann Formula, $$S = k \ln{W}$$ where $k$ is Boltzmann's constant, what happens if $W$ is negative value. If $W$ is a negative value, then it can be rewritten as $$-W = e^{...
0
votes
0answers
12 views

Temperatures necessary for producing spin polarization

As for context, I come from a biology background, and I am trying to self teach myself statistical mechanics through "Statistical Physics - Berkeley Physics Course Volume 5." My question is ...
0
votes
2answers
43 views

Density Of states derivation

In the aspect of density of state derivation or simply assuming the frequency of a solid as a continuous distribution we have to come up with an equation expressing the density of states. Its derived ...
0
votes
0answers
14 views

Entropy change associated with loss of photon

I have a result with no reference which I hope to understand how this result is derived. Say the entropy change associated with the loss of a photon from the incident Bose field is $$ \Delta S = -K \...
0
votes
0answers
18 views

Can I form a generating function for the Laplace transformed cumulants?

Setup: I have the double Laplace transform $\hat{\tilde{p}}(\eta,s)$ of a probability distribution $p(x,t)$ of finding a particle at position $x$ at time $t$, defined by $$ \hat{\tilde{p}}(\eta,s) =...
0
votes
1answer
68 views

Microstates of the system in microcanonical ensemble

Suppose I have a gas enclosed in a thermally insulated box, and so I suppose, this is an example of a system in a micro-canonical ensemble. Now, I want to understand which microstates of the system ...
1
vote
0answers
63 views

Liouville theorem and the ergodic assumption

I am following a course on statistical mechanics. My instructor presented us the following Liouville theorem in two (claimed) equivalent ways: Differential statement: The probability distribution $\...
3
votes
2answers
79 views

Ideal gas law when diatomic molecule is about to break into constituents

Suppose we have a diatomic molecule. Its center of mass has an average kinetic energy given by $$ \frac{1}{2} (m_1 +m_2) v_{cm}^2 = \frac{3}{2}k_BT $$ and using this we can derive the ideal gas law ...
2
votes
1answer
158 views

How to calculate the free energy in curved space?

To study the Hagedorn temperature of string near a black hole, we need to calculate the free energy in curved space. This is can be done calculating a torus path integral, but I want to know if an ...
0
votes
1answer
314 views

Negative absolute pressure with positive absolute temperature

Can the derivative defining pressure $dU \over dV$ or ${∂S \over ∂V}|_{E,N} $ be negative in processes occuring in system not cosmological but statistical (gases or solids or liquids - I mean the ...
2
votes
2answers
197 views

Example of a Carnot machine made of a different physical system than a ideal gas?

Anybody knows an example of a Carnot machine made with any different thing than a gas? For example wire or a magnet. I was wondering that since I read the Kardar's book on Statistical Mechanics. He ...
2
votes
1answer
382 views

The derivation of the Planck distribution

I am trying to understand the Planck distribution and black body radiation. In the Wikipedia derivation of the Planck distribution, the photons confined within a cubic box, are emitting from and ...
1
vote
0answers
24 views

What Gas Law does one get from a Lennard-Jones Potential

Given a potential, at low density we can approximate high order potentials as a sum of two-particle potentials. Given such an approximation, using a Lennard-Jones 6-12 potential, one can obtain a full ...
0
votes
1answer
96 views

Two energy level classical system

Consider a system of $N$ particles obeying classical statistics, each of which can have energy $0$ or $E$. The system is in thermal contact with a reservoir maintained at a temperature $T$. What will ...